1. Field of the Invention
The present invention relates to a method of generating a hybrid grid allowing modelling of a heterogeneous formation crossed by one or more pipes.
The method of more particularly applied to formation of a grid suited to an underground reservoir crossed by one or more wells, in order to model displacements of fluids such as hydrocarbons.
2. Description of the Prior Art
Grid generation is a crucial element for the new generation of reservoir simulators. Grids allow description of the geometry of the geologic structure studied by means of a representation in discrete elements wherein simulation is performed according to a suitable numerical pattern. Better comprehension of physical phenomena requires 3D simulation of the multiphase flows in increasingly complex geologic structures, in the vicinity of types of singularities such as stratifications, faults, pinchouts, channels and complex wells. All this complexity has to be taken into account first by the grid which has to reproduce as accurately as possible to geologic information in its heterogeneous nature.
Grid modelling has made great advances during the past few years in other fields such as aeronautics, combustion in engines, structure mechanics, etc. However, the gridding techniques used in the other fields cannot be applied, as they are, to the petroleum sphere because the professional constraints are not the same. For example, in reservoir simulation, the numerical patterns are constructed from control volumes in order to better respect the mass conservation in the case of transport equations of hyperbolic nature. The grid must be a “block-centered” type grid, that is the nodes must be inside each layer and the boundaries of each block must follow the interface between the layers. Now, if this constraint was not taken into account, the nodes would naturally be placed along the faults and along the stratification boundaries. The consequence of this would be that these interfaces would pass through the control volume that is used. The saturation, constant in the control volume, could not consider discontinuity and the results would not be accurate. It is therefore necessary to develop new techniques that are better suited to requirements of the petroleum field.
Cartesian grids, which are commonly used in current commercial simulators, are not suitable for solving these new problems posed by the development of petroleum reservoirs. Cartesian grids, based on parallelepipedic elements, do not allow representation of such complex geometries.
There is a well-known method of generating structured 3D hexahedral grids of CPG (Corner-Point-Geometry) type which considers the geometry of the bodies, It is described in French patent 2,747,490 (U.S. Pat. No. 5,884,564) filed by the assignee and also in the following publication:
Bennis Ch. Et al. “One More Step in Gocad Stratigraphic Grid Generation: Taking into Account Faults and Pinchouts”; SPE 35526, Stavanger, 1996.
This grid type is more flexible than Cartesian grids because it consists of any hexahedral elements that can be degenerated. It strictly respects the horizons, the faults and it allows representation of certain nonconformities such as pinchouts because its construction is based on these elements. However, this type of grid does not allow solution of all the geometric complexities such as, for example, circular radial grids around complex wells. It is possible to form separately the grid of the reservoir and the girds around the wells but it is difficult to represent several objects in the same CPG type reservoir grid because of connection problems linked with the structured nature of the grid.
Another approach is also known where 3D grids only based on tetrahedral Delaunay elements, with a circular radial refinement around the wells, are automatically generated. The advantages of such an approach is that it is entirely automatic and does not practically not require the user's attention. However, this method has drawbacks which make the results obtained difficult to use:
there are on average five times as many grid cells as in a CPG type grid for the same structure, which is very disadvantageous for simulation calculations,
unlike the structured grids which are easy to visualize, to explore from the inside and to locally modify interactively, it is very difficult and sometimes impossible to properly control the tetrahedral grids because of their size and especially because of their non-structured nature. This poses problems for validating the grid from a geometric point of view as well as for understanding and validating the result of a simulation of this type of grid.
Other approaches are also well-known, which allow generation of grids, notably grids based on control volumes generated from a triangulation (Voronoïand CVFE), associated with techniques of aggregation of the triangles (or tetrahedrons) into quadrangles allowing the number of grid cells to be reduced. Although promising results were obtained with these new grids, precise representation of the geologic complexity of reservoirs and wells remains a subject for research and development. In fact, these grids are rather 2.5D (i.e. vertically projected) and their 3D extension appears to be very difficult. Despite their hybrid aspect, they remain entirely unstructured and would therefore be very difficult to manage and to handle in real 3D. Furthermore, taking account of real 3D faults and deviated wells would greatly increase this difficulty.